Paper: arXiv 2506.16264

Authors: Eckhard Platen

Abstract

The paper summarizes key results of the benchmark approach with a focus on the concept of benchmark-neutral pricing. It applies these results to the pricing of an extreme-maturity European put option on a well-diversified stock index. The growth optimal portfolio of the stocks is approximated by a well-diversified stock portfolio and modeled by a drifted time-transformed squared Bessel process of dimension four. It is shown that the benchmark-neutral price of a European put option is theoretically the minimal possible price and the respective risk-neutral put price turns out to be significantly more expensive.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework for the benchmark approach and benchmark-neutral pricing using Bessel processes and stochastic differential equations. While it includes theoretical derivations and applies historical data for illustrative calibration, it lacks extensive empirical backtesting across multiple markets or asset classes.

Research Flowchart

  flowchart TD
    A[Research Goal: Pricing Extreme-Maturity Options via Benchmark Approach] --> B[Model Stock Index Growth Optimal Portfolio - GOP]
    B --> C[Inputs: Stock Index & Drifted 4D Bessel Process]
    C --> D[Calculate Benchmark-Neutral Price - Minimal Price]
    C --> E[Calculate Standard Risk-Neutral Price]
    D --> F[Outcome: Benchmark-neutral price is theoretically minimal; risk-neutral price is significantly more expensive]
    E --> F